Abstract
In this paper, we consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on the unit sphere such that the mutual distance sum is maximal. It is conjectured that the sum of distances is maximal if the 5 points form a bipyramid distribution with two points positioned at opposite poles of the sphere and the other three positioned uniformly on the equator. We study this problem using interval methods and related techniques, and give a computer-assisted proof.
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Partially supported by a National Key Basic Research Project of China (2004CB318000) and by National Natural Science Foundation of China (61074189).
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Hou, X., Shao, J. Spherical Distribution of 5 Points with Maximal Distance Sum. Discrete Comput Geom 46, 156–174 (2011). https://doi.org/10.1007/s00454-010-9307-7
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DOI: https://doi.org/10.1007/s00454-010-9307-7